The (8–12 Hz) neocortical alpha rhythm is associated with shifts in attention across sensory systems, and is thought to represent a sensory gating mechanism for the inhibitory control of cortical processing. The present preliminary study sought to explore whether alpha frequency transcranial alternating current stimulation (tACS) could modulate endogenous alpha power in the somatosensory system, and whether the hypothesized modulation would causally impact perception of tactile stimuli at perceptual threshold. We combined electroencephalography (EEG) with simultaneous brief and intermittent tACS applied over primary somatosensory cortex at individuals’ endogenous alpha frequency during a tactile detection task (n = 12 for EEG, n = 20 for behavior). EEG-measured pre-stimulus alpha power was higher on non-perceived than perceived trials, and analogous perceptual correlates emerged in early components of the tactile evoked response. Further, baseline normalized tactile detection performance was significantly lower during alpha than sham tACS, but the effect did not last into the post-tACS time period. Pre- to post-tACS changes in alpha power were linearly dependent upon baseline state, such that alpha power tended to increase when pre-tACS alpha power was low, and decrease when it was high. However, these observations were comparable in both groups, and not associated with evidence of tACS-induced alpha power modulation. Nevertheless, the tactile stimulus evoked response potential (ERP) revealed a potentially lasting impact of alpha tACS on circuit dynamics. The post-tACS ERP was marked by the emergence of a prominent peak ∼70 ms post-stimulus, which was not discernible post-sham, or in either pre-stimulation condition. Computational neural modeling designed to simulate macroscale EEG signals supported the hypothesis that the emergence of this peak could reflect synaptic plasticity mechanisms induced by tACS. The primary lesson learned in this study, which commanded a small sample size, was that while our experimental paradigm provided some evidence of an influence of tACS on behavior and circuit dynamics, it was not sufficient to induce observable causal effects of tACS on EEG-measured alpha oscillations. We discuss limitations and suggest improvements that may help further delineate a causal influence of tACS on cortical dynamics and perception in future studies.